A MEASUREMENT ASSURANCE PROGRAM FOR LOW FLOW CALIBRATION BY THE TRANSFER METHOD CS0 JEFF PEERY MAY. 18, 010 This document outlines the Measurement Assurance Program (MAP for Seametrics CS0 flo measurement system a liquid flo measurement system used to calibrate liquid flo meters. It consists of four elements: 1 calibration of measurement devices, statistical process control of measurement system, 3 measurement uncertainty analysis, and 4 a proficiency test. This MAP is responsible for process control, maintaining quality of measurements, and traceability to National Institute of Standards and Technology (NIST standards. MAP s are necessary to maintain quality assurance and ties to national standards [1]. They assure quality of all measurement devices and test procedures and assure a state of statistical control of the measurement process. Upon establishing traceability to national standards a MAP may be implemented to maintain it over time. This document outlines the MAP used to evaluate and manage Seametrics CS0 liquid flo calibration system. La of propagation of error is used to predict measurement uncertainty []. A proficiency test is used to validate the system s measurements. Process control is maintained by Statistical Process Control (SPC [3]. Under this MAP liquid flo rate, volume, and k-factor measurements are traced to NIST and measurement quality is maintained. METHODS Liquid flo meter calibrations are performed by driving liquid ater at constant flo rate through a system of closed conduit and referencing a primary flo meter (meter under test to a secondary flo meter (flo standard. The calibration system is composed of a storage tank, pump, and to secondary flo meters. All components are connected by stainless steel 304 tube. The pump is used to drive fluid from the storage tank to the primary and secondary flo meters; maximum flo rate is approximately 1.6x10-3 m 3 /s and minimum flo rate is approximately 6.31x10-6 m 3 /s. Upstream of the primary and secondary meters are sections of straight pe that are sufficient in length to fully develop flo. Pump motor speed is used to regulate flo rates. Prior to collecting measurements a thermal steady state, hydrodynamic steady state, and test meter output steady state are obtained. After all steady states are obtained volume, time, temperature, and primary and secondary meter output are measured. K-factor, volume, and flo rate measurements are traced to NIST through an unbroken chain of comparisons. Comparisons are created annually by calibrating all measurement devices at an accredited laboratory. Traceability is maintained through SPC. Measurement uncertainty as evaluated by an uncertainty analysis. The entire system as validated by a proficiency test. STATISTICAL PROCESS CONTROL Statistical control of the calibration system is assessed using SPC. The system is calibrated daily against a check standard. Check standard calibrations include to flo rates. Measurements are grouped and plotted using control charts. Control limits are calculated from Shehart s control limit factors [3; Table A.5]. A proficiency test is performed annually using an accredited laboratory, and establishes measurement traceability at that point in time. For all other points in time, SPC maintains confidence in the measurement processes. UNCERTAINTY ANALYSIS La of Propagation of Uncertainty [] as used to determine uncertainty in flo rate, volume, and K- factor measurements. The result as second order accurate (Eq. 1. S S R = 1 + + + n η1 η η n... S 1 (1 here δ as partial differential operator, η as component of measurement process, as uncertainty
of η, S as measurand, and R as measurement uncertainty. The uncertainty analysis as simplified by assuming that liquid temperature as equal to pe temperature. This assumption as valid because Biot number as much less than unity. Conservation of mass as used to derive a function for flo rate (the method is similar to that given by T. T, Yeh et. al [4]. The calibration system as modeled as a completely closed system (no leaks and as broken into three components: 1 storage mass, primary mass and 3 secondary mass. Storage mass as mass contained beteen the secondary and primary meters, secondary mass as total mass seen by the secondary meter (flo standard, and primary mass as total mass seen by the primary meter (meter under test. Assuming that mass as conserved, the difference in mass passing through the primary meter from test start to test end as obtained by equating the total mass at each time. Differences ere expanded by taking the total derivative (Eq.. = ( + VS ρs + ρsvs + VSecρSec + ρsecvsec here ρ as density kg/m 3, V as volume m 3, as the difference operator. Subscripts S, Sec, and Pri refer to Storage volume, Secondary flo meter, and Primary flo meter respectively. Sign of primary and secondary mass depends upon hether the primary flo meter as upstream or donstream of secondary flo meter. Volume and density ere assumed to change ith temperature (Eq. 3-4: V = 3 α T V (3 ρ = α T ρ (4 here T as temperature K, and α as coefficient of thermal expansion 1/K. Equations 3 and 4 ere substituted into equation to obtain an expression for the change in primary mass (Eq. 5. Note that if the primary meter is upstream of the secondary meter, equation 5a is used, else equation 5b is used. here subscripts, and refer to ater and pe material respectively. Volumetric flo rate (Eq. 6 as obtained from equation 5. Q = (6 t ρ here t as time s, and Q bar as average volumetric flo rate m 3 /s. Flo rate uncertainty as determined from equations 1 and 6. Uncertainties (tables I and II represented the 67% probability interval for a standard normal distribution. Uncertainty for k-factor as dependant upon pulse output frequency (for secondary and primary flo meters and time. K-factor uncertainty reported herein as specific to the proficiency test (kfactor as approximately 50,000 ppg. RESULTS Greatest uncertainty in flo rate measurement as approximately 0.48% (Fig. ith coverage factor equal to 3.0x10 0. Greatest uncertainty in k-factor measurement as approximately 0.38% (Fig. ith coverage factor equal to 3.0x10 0. Uncertainty of flo rate as most sensitive to uncertainty of test time, and uncertainty of secondary meter volume. Test time as maintained at 6.0x10 1 seconds. Proficiency test results are listed in table III. Confidence intervals for K-factors measured by Flo Technologies ere ithin the confidence interval for those measured by the CS0. CONCLUSIONS This document outlined the steps taken at Seametrics to establish a MAP for the CS0. Under this program all measurements performed by the transfer system are traceable to NIST. Uncertainty in flo rate, volume, and k-factor ere determined by the la of propagation of error and the calibration system as validated by a proficiency test. = ( Sec + ( α T + 3α T S (5a = ( Sec ( α T + 3α T S (5b
3 REFERENCES [1] B. Belanger, Measurement Assurance Programs Part I: General Introduction, NBS Special Publication 676-I, U.S. Government Printing Office, Washington, May 1984. [] S. J. Kline and F. A. McClintock, Describing Uncertainties in Single-Sample Experiments, Mechanical Engineering, January, 1953. [3] D. J. Wheeler and D. S. Chambers, Understanding Statistical Process Control, SPC Press, Knoxville TN, May 1984. [4] T. T. Yeh et. al., An Uncertainty Analysis of a NIST Hydrocarbon Flo Calibration Facility, Proceedings of the 004 Heat Transfer/Fluids Engineering Summer conference, ASME 004. [5] ANSI/ASTM, Measurement Uncertainty for Fluid Flo in Closed conduits American Society of Mechanical Engineers, 001. [6] F. P. Incropera and D. P. Deitt, Introduction to Heat Transfer John Wiley & Sons, Inc., 1996. [7] Norman E. Doling, Mechanical Behavior of Materials. Prentice Hall, 1999. Jeffrey T. Peery This author as born in Bellevue, Washington, on October 5, 1978. He earned his Bachelor of Science in mechanical engineering in June of 001 and his Master of Science in mechanical engineering in June of 003 from the University of Washington, Seattle, WA. He published his first to papers regarding thermal modeling in biomechanics hile orking at the Veterans Affairs Puget Sound Health Care Center and the Center for Excellence in Limb Loss Prevention and Prosthetic Engineering, during 00 and 004. He currently orks as a mechanical engineer for Seametrics Inc., a designer and manufacturer of mechanical and electro-magnetic liquid flo meters. His ork focuses on flo meter R&D, numerical modeling, design and experimentation.
List of Tables 4 TABLE I THIS TABLE LISTS THE UNCERTAINTY BUDGET FOR TEMPERATURE MEASUREMENTS. Source of Uncertainty Standard Uncertainty Type Degrees of Freedom Electrical Components (% 10 KΩ Resistor 1 1.0x10-1 B 100 KΩ Resistor 1.0x10-1 B 50 KΩ Resistor 3 1.0x10-1 B Voltage supply reference 4.0x10 - B Analog to Digital Conversion Digital Counts 5 1.0x10 1 B Thermistor (K Thermistor calibration 6 1.0x10 - B COMBINED STANDARD UNCERTAINTY: Values ere calculated using the la of propagation of uncertainty (Fig. 1; coverage factor as one and represented the 68% confidence interval. TABLE II THIS TABLE LISTS THE UNCERTAINTY BUDGET FOR VOLUME, K-FACTOR, AND FLOW RATE MEASUREMENTS. Variable Standard Uncertainty Type Degrees of Freedom Temperature (% T 7 3.0 x10-1 B Time (s PLC Scan Time 8 1.7x10 - B PLC Time Resolution 9 1.0x10 - B t 10 1.6x10 - Pulse Count (counts PLC 11 1.16x10 0 A 5 Volume (% V S 3.36x10-1 B Secondary Meter Volume 1 1.5x10-1 B Coefficients of thermal Expansion (K -1 Water 13.8x10-7 B Stainless Steel 304 14 1.x10-9 B Combined standard uncertainty: Values ere calculated using the la of propagation of uncertainty (Fig. ; coverage factor as three and represented the 99% confidence interval. TABLE III THIS TABLE LISTS THE FLOW RATE PROFICIENCY TEST RESULTS. Flo Rate (m 3 Seametrics Accredited Laboratory /s; Test Time (sec Expanded Uncertainty (% Expanded Uncertainty (% (gpm K factor K K=3 factor K=3 4.8075x10-5 ; 0.76 6.0x10 1 5.0099x10 4 3.8x10-1 5.0189x10 4 7.5x10 -.4164x10-5 ; 0.383 6.0x10 1 5.0156x10 4 3.8x10-1 5.030x10 4 7.5x10-1.18x10-5 ; 0.193 6.0x10 1 5.0191x10 4 3.8x10-1 5.0347x10 4 7.5x10-1 3 4 5 6 7 Value ere used from Uncertainty Budget for Temperature (Fig. 1. 8 PLC scan time (one loop through ladder logic code. 9 PLC time resolution. 10 Test Time uncertainty as the RSS of PLC scan time and PLC time resolution. 11 Assumed quantization error as to counts. 1 13 Taken as the smallest tabulated unit of precision from reference 6. 14 Taken as the smallest tabulated unit of precision from reference 7. 15 Flo Technology, Inc.
List of Figures 5 Figure 1 This figure illustrates combined uncertainty in temperature measurements versus actual temperature. Coverage factor as one and represented the 68% confidence interval. Figure This figure illustrates combined uncertainty for volume, k-factor, and flo rate measurements versus flo rate. Coverage factor as three and represented the 99% confidence interval.
6 50500 CS0 Flo Technologies 50400 50300 K-Factor (PPG 5000 50100 50000 49900 0. 0.4 0.6 0.8 Flo Rate (GPM Figure 3 This figure illustrates the proficiency test results. Coverage factor as three and represented the 99% confidence interval